Which expressions are equivalent to the one below? Check all that apply.
49x

LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)

What is  Least Common Multiple?

Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.

We have to factorise 4x²-100 which is of the form A²-B²,

= (2x)² -(10)²

= (2x+10)(2x-10)

= 2×2(x+5)(x-5)

= 4(x+5)(x-5).

We have to factorise 4x + 20​

= 4(x+5)

LCM of 4x²-100 and 4x + 20 = 4(x+5)(x-5).

Hence, LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)

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Answer:

r=21.01 cm

Step-by-step explanation:

2r = diameter

Circumference of a circle = pi 2r

difference = 90

pi2r - 2r =90

 2r (pi-1) =90

90/(2(pi-1) = r = 21.01 cm

Answer:

first three expressions are polynomials and last three are not.

Step-by-step explanation:

last three expression has negative powers of X and  some powers of Xs are not integers.

Answer:

4/7

Step-by-step explanation: Multiply 2/3 x 6/7 Put your answer in lowest terms a. 4/7

Answer:

Difference: 4/21

Step-by-step explanation:

the difference between two quantities is the result of a subtraction

[tex]\frac{6}{7} -\frac{2}{3} =\frac{(6)(3)-(7)(2)}{(7)(3)} =\frac{18-14}{21} =\frac{4}{21}[/tex]

The fraction can no longer be reduced

Hope this helps

Answer:

40 yds^3

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

log a is the same thing as: [tex]log_{10}{a}=b[/tex] which can be rewritten as [tex]10^b=a[/tex] and in general logarithms are in the form [tex]log_ba=c[/tex] which can be written as [tex]b^c=a[/tex]

Rewrite into exponential form

[tex]10^3=5x[/tex]

Simplify exponent

[tex]1000=5x[/tex]

Divide by 5

x=200

Answer:

200

Step-by-step explanation:

I don't know if there are answer choices but the answer is 200

The cost of the file is $6.15 and the cost of the pen is $8.9

The interpretation of the given word problem leads to a system of linear equations.

From the given information:

f + 3p = 32.85 --- (1)

2f + 8p = 83.5 --- (2)

From equation (1)

f = - 3p+32.85

Replace the value of f in the above equation into equation (2)

2(-3p + 32.85) + 8p = 83.5

2p + 65.7 = 83.5

2p = 83.5 -65.7

2p = 17.8

p = 17.8/2

p = 8.9

Replacing the value of p = 8.9 into f = - 3p+32.85

f = -3(8.9)+32.85

f = 6.15

Therefore, we can conclude that the cost of the file is $6.15 and the cost of the pen is $8.9.

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1.  Rewrite one side (or both) by combining like terms. Option C

2. Yes, the equations are equivalent. Option A

1.

Equation A ;  2x -1  = 5x

Equation B ; -1 = 3x

To get equation B from equation A

2x - 1 = 5x

Collect like terms

-1 = 5x -2x

Subtract the like terms

-1 = 3x

Thus, rewrite one side (or both) by combining like terms. Option C

2. 2x - 1 = 5x ...... equation A

Solution ;

2x -5x = 1

-3x = 1

x = -1/3

-1 = 3x

Solution;

x = -1/3

Thus, the equations are equivalent. Option A

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Answer:

The answer is A Find the point-slope form.

y+3= −7/5 ⋅ (x+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The key features of the graph are:

The graph has a minimum value at (-2, -1)

This represents the vertex

The x coordinate of the vertex is the axis of symmetry.

So, we have

x = -2

The graph crosses the y-axis at (0, 3)

This represents the y-intercept

The graph opens up.

This means that the vertex is minimum.

The domain is the set of all real number, because the graph extends in both directions on the x-axis without end

While the range is y >= -1, because it has a minimum at this point

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The solution to the given pair of inequalities is at any point on the line

Inequalities are expressions that are not separated by an equal sign. Given the system of inequalities as shown:

3x-y<2

3y<9x-6

The solution of the system of inequality is the point of intersection of the lines. From the graphed line below, you can see that the point of intersection is at any point on the line since the lines are the same

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The composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.

It should be noted that transformation simply means the manipulation of a shape or geometric figure.

In this case, the composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.

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Step-by-step explanation:

So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where t is typically time in years, and n is how many times it's compounded per year. But in this case it's only compounded 1 time per year so the equation is just [tex]A = P(1+r)^t[/tex]. in this case P is the principal amount, r is the interest, and A is the final amount. So the 5% interest rate becomes 0.05 by dividing by 100 to convert it into decimal form and the principle amount of 11,000. This gives you the formula [tex]A = 11000(1.05)^t[/tex]. This is the answer to the first question where t is the time in years. When it says "Find interest earned" I'm a bit confused, is it giving you x amount of years where you have to calculate the interest earned or does it want a general equation? Because the general equation would be the final amount - the principle amount which calculates the difference. So the equation for interest earned would be [tex]11000(1.05)^t-11000[/tex]. To calculate the amount of money after 5 years you simply plug in 5 as t. this gives you the equation [tex]11000(1.05)^5 \approx 11000(1.276) \approx 14,039.10[/tex]

Equations are written by equating two expressionsThe value of x - 2y is 8/3

Equations are written by equating two expressions. Given the following equation

3x - 6y = 8

Divide through by 3 to have:

3x/3 - 6y/3 = 8/3

x - 2y = 8/3

Hence the value of x - 2y is 8/3

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Step-by-step explanation:

You can't use quadratic formula in this

The answer choice which represents values for which the expression is undefined is; x = -1.

It follows from the task content that the expression in discuss is made up of 2 rational expressions and hence, the value of x which makes the expression undefined is -1 because, upon substitution, we have; (1/0) + (5/0); which yields undefined.

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Answer:

x= 3. x= 0, x= -1

Step-by-step explanation:

Correct on edmentum

Based on the vertices of quadrilateral ABCD and Quadrilateral FGHJ, A. The scale factor is 1/2, and the center of dilation is point A.

First, note the vertices of Quadrilateral FGHJ:

F(1,1)  G(3 ,1)  J (1 , 5)  H(3 , 5)

Find the lengths of the sides of both quadrilaterals:

FG = (3, 1) - (1, 1)                                      AB = (5,1) - (1, 1)  

= (2,0)                                                           = (4, 0)

FH = (3, 5) - (1, 1)                                      AC = (5,9) - (1, 1)  

= (2,4)                                                           = (4, 8)

AB is twice the size of FG.

AC is twice the size of FH

This shows that quadrilateral FGHJ is 1/2 the size of quadrilateral ABCD.

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Answer:

-2

Step-by-step explanation:

3x isnt used because it stated when x>1.

so -2(1) is -2, because x =< 1 is true

Answer:

Step-by-step explanation:

Conditions

Let the circular stones = x

Let the rectangular stones = y

Equations

x + y = 37                          Subtract x from both sides of this equation.

y = 37 - x                           Notice that x is on the right side of the equation

Solution

26x   +  34y = 1138                 Substitute for y

26x + 34(37 - x) = 1138           Remove the brackets

26x + 1258 -34x= 1138           Combine

-8x + 1258 = 1138                    Subtract 1258 from both sides

-8x +1258-1258 = 1138-1258  Combine.  

-8x = -120                                Divide both sides by -8

-8x/-8 = -120/-8

x = 15                                       Two minuses make a plus (last step)

x+ y = 37

15 + y = 37                               Subtract 15 from both sides

15-15 +y = 37-15                     Combine

y = 22

Answer

x = 15     Circular pizza dishes

y = 22   square pizza dishes

The consultant sold 15 circular pizza stones and 22 rectangular pizza stones.

Let's assume the number of circular pizza stones sold is "c" and the number of rectangular pizza stones sold is "r."

We are given two pieces of information:

1. The total number of stones sold: c + r = 37

2. The total amount earned from the sale of the stones: 26c + 34r = 1138

Now, we can use these two equations to solve for the values of "c" and "r."

First, let's use the first equation to express "c" in terms of "r":

c = 37 - r

Now, substitute this value of "c" into the second equation:

26c + 34r = 1138

26(37 - r) + 34r = 1138

962 - 26r + 34r = 1138

Combine the "r" terms:

8r = 1138 - 962

8r = 176

Now, divide by 8 to find the value of "r":

r = 176 / 8

r = 22

Now that we have the value of "r," we can find the value of "c" using the first equation:

c = 37 - r

c = 37 - 22

c = 15

So, the consultant sold 15 circular pizza stones and 22 rectangular pizza stones.

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The first set of integers are: 8 and 32

The second set of integers are: -8 and -32

An integer is a whole number.

It is also the ratio of any real number and 1.

It does not have a decimal part or the decimal part of the integer is zero.

Analysis:

Let the two inters be x and 4x

product of integers  = 4x(x) = 256

4[tex]x^{2}[/tex] = 256

[tex]x^{2}[/tex] = 256/4

[tex]x^{2}[/tex] = 64

x = ±[tex]\sqrt{64}[/tex]

x = -8 0r 8

The other integer = 4 x -8 = -32 or 32

In conclusion the two integers are -8 and -32 or 8 and 32

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Answer:

2 (4+x)

Step-by-step explanation:

4 + x     is  the sum of four and a number 'x'   now multiply by 2

2  ( 4+ x)

Answer: A

Step-by-step explanation:

Letting [tex]f(y)=x[/tex],

[tex]x=\sqrt{y}-5\\\\x+5=\sqrt{y}\\\\y=(x+5)^{2}[/tex]

Also, the domain of an inverse is the same as the range of the original function, so the range is [tex]x \geq 0[/tex]

We can rewrite the given expression to:

[tex]4*\sqrt{x - 2} - 3[/tex]

So the correct option is the third one.

Here we have the expression:

[tex]\sqrt{16x - 32} - 3[/tex]

Taking the 16 as a common factor inside the square root:

[tex]\sqrt{16*(x - 2)} - 3[/tex]

and 16 = 4², then:

[tex]\sqrt{16*(x - 2)} - 3 = \sqrt{4^2*(x - 2)} - 3\\\\4* \sqrt{(x - 2)} - 3[/tex]

Now, if the parent function is:

[tex]y = 4*\sqrt{x}[/tex]

Our function is the parent function translated 2 units to the right and 3 units down. The correct option is the third one

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By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.

In trigonometry, an unit circle is a circle with a radius of 1 and used to determine the values of trigonometric functions. There are two fundamental trigonometric functions: (i) sine, (ii) cosine, and the tangent is a derivate trigonometric function, which is defined below:

tan θ = y/x     (1)

If we know that x = 1 and y = 0, then the tangent of the terminal point of angle is:

tan θ = 0/1

tan θ = 0

By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.

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Answer:

tan= 0

Step-by-step explanation:

^^^correct :)

Answer:

4/1 or 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

[tex]\frac{\frac{6}{7} }{\frac{3}{14} } =\frac{(6)(14)}{(7)(3)} =\frac{84}{21} =4[/tex]

Hope this helps

H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.

A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.

Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.

Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .

S = “On input (M, B)

This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.

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Answer:

67

Step-by-step explanation:

7 + 2 =9

9 + 4 = 13

13 + 16 = 29

29 + 38 = 67

The graph is in the attached image.